What is the integral of (1+sin(x))/(x^2) ?

The integral of (1+sin(x))/(x^2) is -(1+sin(x))/x+\Ci(x)+C

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integral of (1+sin(x))/(x^2)

\int \frac{1 + sin ( x )}{x ^{2}} d x

- \frac{1 + sin ( x )}{x} + Ci (x) + C

Solution steps

\int \frac{1 + sin ( x )}{x ^{2}} d x

Apply Integration By Parts

= - \frac{1 + sin ( x )}{x} - \int - \frac{cos ( x )}{x} d x

\int - \frac{cos ( x )}{x} d x = - Ci (x)

= - \frac{1 + sin ( x )}{x} - (- Ci (x))

Simplify

= - \frac{1 + sin ( x )}{x} + Ci (x)

Add a constant to the solution

= - \frac{1 + sin ( x )}{x} + Ci (x) + C

\int x^{2} + 7 d x

\int \frac{1}{5 x - 1} d x

\int 2 (2 x - 1)^{3} d x

\int x e^{\frac{2 x}{3}} d x

\int - \frac{1}{x ( ln ( x ) ) ^{2}} d x

What is the integral of (1+sin(x))/(x^2) ?
The integral of (1+sin(x))/(x^2) is -(1+sin(x))/x+\Ci(x)+C